For the past 𝑚 days, the average daily production at a company was 100 units per day. If today’s production of 180 units changes the average to 110 units per day, what is the value of 𝑚?

The correct option is 7.

To find the value of
$m$
, we can use the relationship between the average daily production, the total number of units produced, and the number of days.

Step 1: Express the total production of the past
$m$
days.
The average production over the past
$m$
days was 100 units per day. Therefore, the total production for this period is the average multiplied by the number of days:

$$\text{Total Production for past}m\text{days}=100m$$

Step 2: Express the new total production and the new number of days.
Today, an additional 180 units were produced. This increases the total production to:

$$\text{New Total Production}=100m+180$$

The total number of days, including today, is now:

$$\text{New Number of Days}=m+1$$

Step 3: Set up the equation using the new average.
We are given that today's production changes the overall average to 110 units per day. We can write the average formula as:

$$\frac{100m+180}{m+1}=110$$

Step 4: Solve for
$m$
.
Multiply both sides of the equation by
$\left(m+1\right)$
to clear the fraction:

$$100m+180=110(m+1)$$

Distribute 110 on the right side of the equation:

$$100m+180=110m+110$$

Subtract
$100m$
from both sides:

$$180=10m+110$$

Subtract 110 from both sides:

$$70=10m$$

Divide both sides by 10 to find
$m$
:

$$m=7$$

Thus, the value of
$m$
is 7.